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Final report
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17 It is worth pointing out that the settling velocity for droplets in the size range 100-200 microns
is 0.2 to 0.8 m/s. This means that droplets this size may remain airborne for a time of order
1-5 seconds during which they may be convected a distance of order 10 metres from the base
of the tank. This means that some liquid droplets may remain suspended in the vapour flow as it
impacts on the bund wall or other tanks within the bund.
Air entrainment
18 Jets of air or buoyant plumes entrain air through the action of shear driven vortices. A dense
liquid cascade entrains air in a different, somewhat less complex way. Individual falling drops
drag the air within the cascade downwards and air is drawn in through the sides to compensate.
There are shear forces and induced vortices at the edge of the cascade but if the cross section is
large these processes make little difference to the total volume flux of air – which is the quantity of
primary interest.
19 A comparison has been made of detailed CFD predictions, which have included all the
aerodynamic processes involved in falling sprays, and a simple momentum conservation model
which ignores the induced shear flow on the spray periphery. This has shown that for the
scenarios considered here it is adequate to use the latter, simpler treatment, which is described in
Annex 1. Typical results obtained using the simple momentum conservation model are shown in
Figure 16. In overfilling incidents the mass flux density is likely to be in the range 1 to 10 kg/m
2
/s.
This corresponds to maximum droplet velocities of 10-13 m/s and vapour velocities of 4-6 m/s.
20 CFD methods of the sort reported in Section 3 are capable of calculating droplet and vapour
velocities both in the liquid cascade and in the vapour flow spreading out from the foot of the
tank. These calculations fully encompass exchange of mass, heat and momentum between liquid
and vapour phases.
Vaporisation of liquid
21 The fineness of liquid dispersal controls the extent to which liquid and vapour approach
thermodynamic equilibrium. Example results from a CFD study of heat and mass transfer in the
cascade are shown in Figure 17.
Droplet dynamics in spray of varying mass density
0
2
4
6
8
10
12
14
16
18
20
0
5
10
15
20
Distance below origin (m)
droplet velocity (m/s)
Free fall
100 kg/s/m2
10 kg/s/m2
1 kg/s/m2
0.1 kg/s/m2
0.01 kg/s/m2